How to convert hexadecimal numbers to decimal numbers

First convert to binary (except 16 remainder), then convert binary to decimal.

Decimal base 10123 = 1 * (102 power) + 2 * (101 power) + 3 * (100 power) = 100 + 20 + 3

I understand. The same goes for hexadecimal base 16

6d = 6 * (161 power) + d * (160 power) = 6 * 16 + 13 = 96 + 13 = 109

The rest of the data is calculated.

(1) Hexadecimal to decimal method:

Use single digits + tens * 16 + hundreds * 256 + thousands * 4096 +...When multiplied, the number multiplied by the first single digit is 16 times the number multiplied by the number of the last single digit of ten.

The specific cases are as follows:

ab)=a×16+b=(171)

abc)=a×256+b×16+c=(2748)<>

b) The method of decimal to hexadecimal.

Convert decimal to hexadecimal and divide by 16 until the quotient is 0. (The specific usage is shown in the figure below) <>

The specific algorithm for converting hexadecimal to decimal is:

First of all, understand the hexadecimal number (from right to left the number is the 0th, 1st, 2nd......The 0th place has a weight of 16 to the power of 0, the first place has a weight of 16 to the 1st power, and the 2nd place has a weight of 16 to the 2nd power, and so on.

Understand that the binary numbers represented by ABCDEF are 10, 11, 12, 13, 14, and 15.

The formula for converting hexadecimal to decimal is to multiply each binary number by the corresponding power of 16 from right to left, and then add the numbers together.

There is a basic principle when it comes to base conversion:

The amount of "amount" expressed after conversion cannot be changed. There are as many 111 apples in binary as there are 7 apples in decimal.

The arrangement of digits in decimal is ...... like thisThousands of tenths ......

The digit arrangement in the base R system is ...... like thisr^4 r^3r^2 r^1 r^0 r^-1 r^-2 r^-3……

The primary square of the decimal phase between adjacent digits can be seen.

Just press the right. There are sample questions in the book.

**If you don't understand, ask for help again.

First, the idea of conversion analysis: 4 base 2 bits for a 16 base number, base 1111 for 16 base F, 1 = 8 in the base 2 thousand, 1 = 4 in the 100 place, 1 = 2 in the 10 place, 1 = 1 in the single place, the number of each bit is converted accordingly and then added, the number to the number is the base 10 number 0-15, which can be easily converted into hexadecimal. If 01011100 can be seen as two sets of base numbers 0101 and 1100, then this number is the hexadecimal 5c.

2. Example: With bit-weighted multiplication, product addition is relatively simple. For example, 8ffc035b is converted to decimal (the lowest digit is 16 0, in order to the left):

ffc035b(16)=8x16^7+fx16^6+fx16^5+cx16^4+0x16^3+3x16^2+5x16^1+bx16^0

2、=2147483648+15x16^6+15x16^5+12x16^4+0+768+80+11

3. About binary.

1. Binary is a number system widely used in computing technology. Binary data is a number represented by two numbers, 0 and 1. Its cardinal number is 2, the carry rule is "every two into one", and the borrowing rule is "borrow one to become two", which was discovered by Leibniz, a German master of mathematical philosophy in the 18th century.

Current computer systems use basically binary systems, and data is stored in computers mainly in the form of complements. Binary in a computer is a very tiny switch, with "on" for 1 and "off" for 0.

Century is known as one of the important symbols of the third scientific and technological revolution of the invention and application of the computer, because the digital computer can only recognize and process by '0''1' symbol string. The mode of operation is binary.

The 19th-century Irish logician George Bull's thought process on logical propositions was translated into pairs of symbols"0''.1''In some kind of algebraic calculus, binary is a base system that is a base of every 2 digits.

Because it uses only two number symbols, it is very simple and convenient and easy to implement electronically.

Hexadecimal conversion.

Decimal method: "sum by weight", e.g. hexadecimal: (2af5)h=2*16 3+10*16 2+15*16 1+5*16 0=8192+2560+240+5=10997.

Hexadecimal is a representation of data in a computer. It's not the same as the representation in our daily lives.

It consists of 0-9, a-f, and the letters are not case sensitive. The correspondence with decimal is: 0-9 corresponds to 0-9; a-f corresponds to 10-15; Numbers in base can be represented by numbers of 0 (n-1) and letters a-f over 9.

The decimal system, i.e. full ten into one, full twenty into two, and so on ......According to the right, the first right is 10 0, and the second place is 10 1 ......And so on, the nth digit 10 (n-1), the value of this number is equal to the sum of the value of each bit * the corresponding weight of that bit.

The base system, also known as the carry counting system, is an artificially defined counting method with carry (there are counting methods without carrying, such as the original knotted rope counting method, the "positive" word counting method commonly used when singing tickets, and similar tally mark counting). For any kind of decimal --- base, it means that the number in each position is calculated every x digit. Decimal is every 10, and hexadecimal is 1 every 16, binary.

It is every two into one, and so on, the base X system is every X round.